Setting field of view in Blender 2.8 from half angles of horizontal and vertical field of view of camera
I found what I was looking for from https://blender.stackexchange.com/a/40835/99643 .
The following equations were helpful from that answer:
sensor_width_in_mm = $K[1,1]*K[0,2] / (K[0,0]*K[1,2])$
$s_u$ = resolution_$x$_in_px / sensor_width_in_mm
focal_length_in_mm = $K$[$0,0$] / $s_u$